Discrete Optimization: The Case of Generalized BCC Lattice

Recently, operations research, especially linear integer-programming, is used in various grids to find optimal paths and, based on that, digital distance. The 4 and higher-dimensional body-centered-cubic the nD (n≥4) equivalent of 3D body-centered cubic grid, a well-known grid from solid state physics. These consist integer points such that parity all coordinates are same: either odd or even. A popular type distance, chamfer which paths. There two types neighbors (closest same closest different point-pairs), weights for steps between fixed. Finding minimal path an integer-programming problem. First, we solve its programming relaxation. found if this solution integer-valued. Otherwise, Gomory-cut applied obtain optimum. Using special properties optimization problem, determined cases positive weights. geometry described by Hilbert basis non-negative part kernel space matrix steps.